Exploratory analysis of the Albury time series data
Anna Quaglieri
Setup
Water level data
The data below refer to the historical data set of water at Murray basin at Albury back from 1885 (lat -36.0981, long 146.9065). The dataset is available through the Amphora website at https://beta.amphoradata.com/Amphorae/Detail?id=5602eb66-fb21-4350-9f68-0e5cbb925f62.
Time series of water level/salinity/temperature data
> p1=twater %>%
+ feasts::autoplot(wlevel) + ggtitle("Water level at Albury along the Murray river") + theme_classic()+ labs(x = "Years",y="Level (m)")
>
> p2=twater %>%
+ feasts::autoplot(wtemp) + theme_classic()+ labs(x = "Years",y="Temperature (Deg C)")
>
> p3=twater %>%
+ feasts::autoplot(wsal) + theme_classic() + labs(x = "Years",y="Salinity (uS/cm)")
>
> plot_grid(p1,p2,p3,nrow=3)
> twater %>%
+ feasts::autoplot(wlevel) +
+ autolayer(filter_index(twater, "2001-01-01" ~ "2007-12-31"), color = "#de2d26") +
+ ggtitle("Water level at Albury along the Murray river. Drought years 2001-2007 highlighted in red.") +
+ theme_bw()+ labs(x = "Years",y="Level (m)")## Plot variable not specified, automatically selected `.vars = wlevel`
Zoomed time series of water salinity/temperature data
> p3=twater %>%
+ filter(year(Date) > 2000) %>%
+ autoplot(wlevel) + ggtitle("Water level after year 2000") + theme_bw()+
+ autolayer(filter_index(twater, "2015-01-01" ~ "2016-01-01"), color = "#de2d26") +
+ labs(x = "Years",y="Level (m)")## Plot variable not specified, automatically selected `.vars = wlevel`> p1=twater %>%
+ filter(year(Date) > 2000) %>%
+ autoplot(wtemp) + ggtitle("Water temperature after year 2000") + theme_bw()+
+ autolayer(filter_index(twater[,c("Date","wtemp")], "2015-01-01" ~ "2016-01-01"), color = "#de2d26") +
+ labs(x = "Years",y="Temperature (Deg C)")## Plot variable not specified, automatically selected `.vars = wtemp`> p2=twater %>%
+ filter(year(Date) > 2000) %>%
+ autoplot(wsal) + ggtitle("Water salinity after year 2000") + theme_bw() +
+ autolayer(filter_index(twater[,c("Date","wsal")], "2015-01-01" ~ "2016-01-01"), color = "#de2d26") +
+ labs(x = "Years",y="Salinity (uS/cm)")## Plot variable not specified, automatically selected `.vars = wsal`> plot_grid(p3,p1,p2,nrow=3)
Time series of water level data by year
> twater %>%
+ gg_season(wlevel, colour = "black",alpha=0.5) + ggtitle("Water level time series by intervals") +
+ theme_bw() +
+ facet_wrap(~interval) + theme(legend.position = "none")+ labs(x = "Months",y="Level (m)")
> twater %>%
+ filter(year(Date) > 2009) %>%
+ mutate(year = year(Date)) %>%
+ gg_season(wsal,colour="black") + ggtitle("Water Salinity, between 2010-2019") + theme_bw()+
+ labs(x = "Years",y="Salinity (uS/cm)")+ theme(legend.position = "none") +
+ facet_wrap(~year)
> twater %>%
+ filter(year(Date) > 2000) %>%
+ mutate(year = year(Date)) %>%
+ gg_season(wtemp,alpha=0.7) +
+ ggtitle("Water temperature, between 2001-2019") + theme_bw()+
+ labs(x = "Years",y="Temperature (Deg C)") + theme(legend.position = "bottom")
Correlations between water level and temperature/salinity
> # Water levels vs water temperature
> twater %>%
+ mutate(year = year(Date),
+ month = month(Date),
+ day = day(Date)) %>%
+ filter(year >= 2000) %>%
+ mutate(Year = factor(year(Date))) %>%
+ ggplot(aes(x = wlevel, y = wtemp,colour=Year)) +
+ geom_point(alpha=0.3,colour="grey") +
+ geom_smooth(se=FALSE)+
+ theme_bw() +
+ ggtitle("Water level vs water temperature (>2000)") +
+ labs(x = "Water level (m)", y = "Water temperature (Deg C)") +
+ theme(legend.position = "bottom")+
+ scale_color_viridis_d()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
> # Water levels vs water salinity
> twater %>%
+ filter(year(Date) > 2009) %>%
+ mutate(Year = factor(year(Date))) %>%
+ ggplot(aes(x = wlevel, y = wsal,colour=Year)) +
+ geom_point(alpha=0.3) +
+ geom_smooth(se=FALSE) +
+ theme_bw()+
+ labs(x = "Water level (m)", y = "Water salinity (uS/cm)") +
+ ggtitle("Water level vs water salinity (>2010)") ## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
> # Water levels vs water salinity
> twater %>%
+ filter(year(Date) > 2000) %>%
+ mutate(Year = factor(year(Date)),
+ Month = factor(month(Date))) %>%
+ ggplot(aes(x = wlevel, y = wsal,colour=Month)) +
+ geom_point(alpha=0.5) +
+ theme_bw()+
+ labs(x = "Water level (m)", y = "Water salinity (uS/cm)") +
+ ggtitle("Water level vs water salinity (>2010)")
Scatterplot without stratifying by year/month
> # Water levels vs water salinity
> twater %>%
+ filter(year(Date) > 2000) %>%
+ mutate(Year = factor(year(Date))) %>%
+ ggplot(aes(x = wlevel, y = wsal)) +
+ geom_hex(bins = 70) +
+ scale_fill_continuous(type = "viridis") +
+ theme_bw()+
+ labs(x = "Water level (m)", y = "Water salinity (uS/cm)") +
+ ggtitle("Water level vs water salinity (>2010)")
> # Water levels vs water salinity
> twater %>%
+ filter(year(Date) > 2000) %>%
+ mutate(Year = factor(year(Date))) %>%
+ ggplot(aes(x = wlevel, y = wtemp)) +
+ geom_hex(bins = 70) +
+ scale_fill_continuous(type = "viridis") +
+ theme_bw()+
+ labs(x = "Water level (m)", y = "Water temperature (Deg C)") +
+ ggtitle("Water level vs water temperature (>2010)")
> # Water levels vs water salinity
> plot_sal <- twater %>%
+ filter(year(Date) > 2000) %>%
+ mutate(Year = factor(year(Date)))
>
> plot_sal %>%
+ ggplot(aes(x = wlevel, y = log2(wsal))) +
+ geom_point(alpha=0.3) +
+ geom_smooth(se=FALSE) +
+ geom_point(data = subset(plot_sal, Year %in% "2015"),colour="#de2d26",alpha=0.3) +
+ theme_bw()+
+ labs(x = "Water level (m)", y = "Water salinity (uS/cm)") +
+ ggtitle("Water level vs water salinity (>2010).\nYear 2015 highlighted in red")## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
> # Water levels vs water salinity
> twater %>%
+ filter(year(Date) > 2000) %>%
+ mutate(Year = factor(year(Date)),
+ Month = factor(month(Date))) %>%
+ ggplot(aes(x = wlevel, y = wsal)) +
+ geom_hex(bins=20) +
+ scale_fill_continuous(type = "viridis") +
+ theme_bw()+
+ facet_wrap(~Month) +
+ labs(x = "Water level (m)", y = "Water salinity (uS/cm)") +
+ ggtitle("Water level vs water salinity (>2010)")
Min/max water temperature
> min_max <- twater %>%
+ as.data.frame() %>%
+ mutate(Year = year(Date)) %>%
+ filter(Year > 2000) %>%
+ group_by(Year) %>%
+ summarise(min_temp = min(wtemp,na.rm=TRUE),
+ max_temp = max(wtemp, na.rm=TRUE)) %>%
+ gather(key = summary, value = wtemp, min_temp,max_temp)> ggplot(min_max, aes(x = Year, y = wtemp,colour=summary)) + geom_point() +
+ geom_line() + theme_bw()
Lag plots
> p1.data <- twater %>%
+ filter(year(Date) > 2017) %>%
+ mutate(lag30.wlevel = c(diff(wlevel,lag=30),rep(NA,30)),
+ lag30.wtemp = c(diff(wtemp,lag = 30),rep(NA,30))) %>%
+ gather(key = measure, value = level,lag30.wlevel:lag30.wtemp)
>
> p1=twater %>%
+ filter(year(Date) > 2018) %>%
+ autoplot(wlevel)
> p2=twater %>%
+ filter(year(Date) > 2018) %>%
+ autoplot(wtemp)
> plot_grid(p1,p2,nrow=2)